On an elliptic Kirchhoff-type problem depending on two parameters

In this paper, on a bounded domain Omega subset of R(n), we consider a non-local problem of the type {-K(integral(Omega) vertical bar del u(x)vertical bar(2)dx)Delta u = lambda f(x,u) + mu g(x,u) in Omega u=0 on partial derivative Omega. Under rather general assumptions on K and f, we prove, in particular, that there exists lambda > lambda* such that, for each lambda > lambda* and each Caratheodory function g with a sub-critical growth, the above problem has at least three weak solutions for every mu >= 0 small enough.